Porous crystalline metal-organic frameworks (MOFs) or porous coordination polymers (PCPs) are emerging as a new class of proton conductors with numerous investigations. Some of the MOFs exhibit an excellent proton-conducting performance (higher than 10-2 S cm-1) originating from the interesting hydrogen(H)-bonding networks with guest molecules, where the conducting medium plays a crucial role. In the overwhelming majority of MOFs, the conducting medium is H2O because of its degenerate conjugate acid-base system (H3O+ + H2O ⇔ H2O + H3O+ or OH- + H2O ⇔ H2O + OH-) and the efficient H-bonding ability through two proton donor and two acceptor sites with a tetrahedral geometry. Considering the systematic molecular similarity to water, ammonia (NH3; NH4 + + NH3 ⇔ NH3 + NH4 +) is promising as the next proton-conducting medium. In addition, there are few reports on NH3-mediated proton conductivity in MOFs. In this perspective, we provide overviews of the degenerate water (hydronium or hydroxide)- or ammonia (ammonium)-mediated proton conduction system, the design strategies for proton-conductive MOFs, and the conduction mechanisms.